Season the chicken cubes with salt and pepper. Melt butter in a large pot or Dutch oven over medium-high heat, then add the chicken and cook until golden brown and cooked through, about 5-7 minutes. Remove the chicken from the pot and set aside.
In the same pot, add the minced garlic and cook for about 30 seconds until fragrant, scraping up any browned bits from the bottom of the pot.
Pour in the chicken broth and bring to a boil. Add the fettuccine, pressing it down to submerge it in the liquid. Reduce heat to a simmer, cover, and cook for about 10-12 minutes, or until the pasta is al dente, stirring occasionally to prevent sticking.
Reduce the heat to low. Stir in the heavy cream and grated Parmesan cheese. Continue stirring until the cheese is melted and the sauce has thickened, about 1-2 minutes.
Return the cooked chicken to the pot. Stir everything together to coat the chicken and pasta in the sauce. Season with additional salt and pepper to taste.
Remove from heat, garnish with fresh parsley, and serve immediately with extra Parmesan cheese if desired.